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arXiv:1207.5936 · Physical Review A

Multipole analysis of radio-frequency reactions in ultracold atoms

Betzalel Bazak, Evgeny Z. Liverts, Nir Barnea

Published Oct 10, 2012• 6 citations
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Abstract

Using the multipole expansion, we analyze photoinduced reactions in an ultracold atomic gas composed of identical neutral bosons. While the Franck-Condon factor dominates the photoinduced spin-flip reactions, we have found that for a frozen-spin process in which the atomic spins are conserved, the reaction rate is governed by the monopole ${r}^{2}$ and the quadrupole terms. Consequently, the dependence of the frozen-spin reaction rate on the photon wave number $k$ acquires an extra ${k}^{4}$ factor in comparison to the spin-flip process. Comparing the relative strength of the ${r}^{2}$ and quadrupole modes in dimer photoassociation, we predict that the mutual importance of these two modes changes with temperature and scattering length.

DOI
10.1103/physreva.86.043611

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Using the multipole expansion, we analyze photoinduced reactions in an ultracold atomic gas composed of identical neutral bosons. While the Franck-Condon factor dominates the photoinduced spin-flip reactions, we have found that for a frozen-spin process in which the atomic spins are conserved, the reaction rate is governed by the monopole r2{r}^{2}r2 and the quadrupole terms. Consequently, the dependence of the frozen-spin reaction rate on the photon wave number kkk acquires an extra k4{k}^{4}k4 factor in comparison to the spin-flip process. Comparing the relative strength of the r2{r}^{2}r2 and quadrupole modes in dimer photoassociation, we predict that the mutual importance of these two modes changes with temperature and scattering length.
Using the multipole expansion we analyze photo induced reactions in an ultra-cold atomic gas composed of identical neutral bosons. While the Frank-Condon factor dominates the photo induced spin-flip reactions, we have found that for frozen-spin process the reaction rate is governed by the r2r^2r2 and quadrupole terms. Consequently, the dependence of the frozen-spin reaction rate on the photon wave number kkk acquires an extra k4k^4k4 factor in comparison to the spin-flip process. Comparing the relative strength of the r2r^2r2 and quadrupole modes in dimer photoassociation we predict that the mutual importance of these two modes changes with temperature and scattering length.
Abstract In view of recent experiments in ultracold atomic systems, the photoassociation of Efimov trimers, composed of three identical bosons, is studied utilizing the multipole expansion. We study both the normal hierarchy case, where one-body current is dominant, and the strong hierarchy case, relevant for photoassociation in ultracold atoms, where two-body current is dominant. For identical particles in the normal hierarchy case, the leading contribution comes from the r 2 s -mode operator and from the quadrupole d -mode operator. The s -mode reaction is found to be dominant at low temperature, while as the temperature increases the d -mode becomes as significant. For the strong hierarchy case, the leading contribution comes from a 2-body s -wave δ operator. In both cases log periodic oscillations are found in the cross section. For large but finite scattering length the amplitude of the oscillations becomes larger in comparison to infinite scattering length case. We apply our theory to photoassociation of 7 Li ultracold atoms and show a good fit to the available experimental results.
Ultracold collisions of neutral atoms and molecules have been of great interest since experimental advances enabled the cooling and trapping of such species. This study develops a simplified theoretical treatment of a low-energy collision between an alkali atom and a diatomic molecule accompanied by absorption of a photon from an external electromagnetic field. The long-range interaction between the two species is treated, including the atomic spin–orbit interaction. The long-range potential energy curves for the triatomic complex are calculated in realistic detail, while effects of the short-range behavior are mimicked by applying different boundary conditions at the van der Waals length. For neutral colliding species, the leading interaction term is the dipole–dipole interaction. In the case of nonpolar dimers like Cs 2, the second leading term is the quadrupole–quadrupole interaction. However, there is also a strong dipole–quadrupole interaction for dimers with a large permanent dipole moment such as NaCs, making the dipole–quadrupole interaction the second leading term for an atom colliding with a polar dimer. Our applications of the simplified treatment show a higher density of trimer states for a polar dimer compared to the case of a nonpolar dimer like Cs 2 . This is a consequence of the strong quadrupole–dipole coupling between the atom and the dimer dipole moment.
We study the atom-dimer collision reaction for a three bosonic 7Li^{7}\mathrm{Li}7Li system using a multichannel model. We calculate the atom-dimer scattering length and dimer relaxation rate for all three 7Li^{7}\mathrm{Li}7Li atoms in $|f=1,{m}_{f}=1\ensuremath{\rangle}$ (case I) or $|f=1,{m}_{f}=0\ensuremath{\rangle}$ (case II) in an external magnetic field. The dimer is considered as the Feshbach dimer in both cases. In case I there are two atom-dimer resonances, whereas in case II only one atom-dimer resonance induced by the second excited trimer state is observed. It is found that ddd-wave two-body interaction plays an appreciable role in the entire considered magnetic field regime in case I but only when B>B>B> 890 G in case II. We calculate the state-to-state transition probability and normalized transition probability from the incoming atom-dimer channel to the deep atom-dimer hyperfine channel. A propensity that the second-deepest hyperfine channels of atom-dimer collision reaction are dominant in all product channels is revealed for both sss- and ddd-wave dimers.
We study the manifestations of universal four-body physics in ultracold dimer-dimer collisions. We show that resonant features associated with three-body Efimov physics and dimer-dimer scattering lengths are universally related. The emergence of universal four-boson states allows for the tunability of the dimer-dimer interaction, thus enabling the future study of ultracold molecular gases with both attractive and repulsive interactions. Moreover, our study of the interconversion between dimers and Efimov trimers shows that B2+B2-->B3+B rearrangement reactions can provide an efficient trimer formation mechanism. Our analysis of the temperature dependence of this reaction provides an interpretation of the available experimental data and sheds light on the possible experimental realization of rearrangement processes in ultracold gases.
This thesis has investigated the dynamics of ultracold atomic collisions in the presence of both static magnetic and oscillating radio-frequency (rf) fields. The bound state structure and scattering length of 39K+133Cs was examined in the presence of only a static magnetic field, where it was found that no Feshbach resonance of suitable width for magnetoassociation existed at a magnetic field where caesium can be cooled to degeneracy. We then showed that zero-energy Feshbach resonances may be engineered using an rf field in places where they did not previously exist. An rf field with frequency 79.9 MHz was chosen to induce a resonance near 21 G. The widths of such rf-induced Feshbach resonances increase quadratically with rf field strength. The resonances presented are lossless with circularly polarized rf, and the molecules created are long-lived even with plane-polarized RF. Collisional losses in rf-dressed magnetic traps were also investigated. An rf-induced loss mechanism that does not exist in the absence of rf radiation was identified. This mechanism is not suppressed by a centrifugal barrier in the outgoing channel, and can be much faster than spin relaxation, which is centrifugally suppressed. We explore the dependence of the rf-induced loss rate on singlet and triplet scattering lengths, hyperfine splittings and the strength of the rf field. The results were interpreted in terms of an adiabatic model of the collision dynamics, and calculate the corresponding nonadiabatic couplings. The loss rate can vary by 10 orders of magnitude as a function of singlet and triplet scattering lengths. 87Rb is a special case, where several factors combine to reduce rf-induced losses; as a result, they are slow compared to spin-relaxation losses. For most other alkali-metal pairs, rf-induced losses are expected to be much faster and may dominate. For heteronuclear mixtures an rf-modified spin-exchange mechanism was identified that results in loss rates orders of magnitude greater than the rf-induced loss rates in homonuclear cases. Fast loss is expected in mixtures where the Lande g-factors differ.